But specialists in the Federal Bureau of Investigation (FBI) didn't take Mr. Mikheyev's activities lightly. What he demonstrated - along with two other colleagues who were nabbed over the past three weeks by the FBI - was that while Soviet spies can be clumsy, they are also incredibly persistent. On the whole, they have grown more sophisticated over the years. And when it comes to buying or stealing American high technology secrets, they have scored a number of highly damaging successes.

The FBI recently announced that in addition to Mikheyev, two other Soviet officials were being asked to leave the United States because of espionage. According to the FBI:

* Lt. Col. Yevgeniy N. Barmyantsev, a Soviet military attache in Washington, was seized on April 16 as he took eight rolls of 35-millimeter film containing photographs of classified documents from the hollow of a tree in rural Montgomery County, Md. He was said to be attempting to obtain US military and technological secrets.

* Oleg V. Konstantinov, an intelligence officer attached to the Soviet mission to the United Nations, was caught April 2 on Manhasset, Long Island, when, in an effort to obtain aerospace secrets, he met with an American who had operated under the control of the FBI for several years.

All three men were products of a system that, while highly sophisticated in its use of computers and code-breaking techniques, still places enormous stress on the deployment of human spies. As one defector from the KGB, the chief Soviet intelligence agency, once put it, the Soviets do not like to place too much emphasis on technology in their intelligence gathering. They consider it of the highest importance to work on the human failings of their chief opponents, the Americans, and to try to obtain documents - what the defector described as ''the kind of thing you can feel and touch.''

In this game of spies, which goes on now much as it did during the Cold War years, FBI officials have been saying for some years that the US is outnumbered. At one point last year, a top-level FBI official said that FBI money and manpower was stretched to the point where the bureau had to stop surveillance of certain known Soviet spies.

It appears that in the last year or so, the FBI obtained congressional authorization for additional funds. But there is a constant tug of war within the Justice Department over such funds. The precise amount going to counter-espionage is kept secret.

FBI spokesman Roger Young recently asserted once again, ''We're pretty well outnumbered in this game.'' Mr. Young said Mr. Zimmerman had set an example of what is needed to help the FBI. Zimmerman consulted with the congresswoman for whom he works, Republican Olympia Snowe from Maine, and then notified the FBI that he had been contacted by Mikheyev. The FBI instructed Zimmerman to find out what Mikheyev wanted, and Zimmerman used a hidden microphone to record conversations with Mikheyev.

Soviet efforts to penetrate Capitol Hill have been going on for years, so there was nothing particularly new in Mikheyev's approach. Three earlier attempts to recruit congressional aides are on public record. In the late '60s and early '70s, two staff members in the Senate and House were used by the FBI as double agents, pretending to work for the Soviets, but actually working against them.

But the Soviets' biggest single source of intelligence is probably material that is publicly available. And despite any number of expulsions around the world, the Soviets keep pouring in the human spies. The FBI estimates that of an estimated 2,500 Soviet citizens now living in this country, somewhere between 25 to 45 percent are engaged in intelligence gathering.

''They can send waves of people over here with the idea of 'let's see what we can get,''' says Zimmerman. ''They can just keep trying, with the knowledge that they may be expelled, but that they probably won't be punished in any other way.''

Zimmerman says that Aleksandr Mikheyev, who had come down to Washington from the Soviet mission at the United Nations, told the congressional aide he was studying agricultural economics. He was introduced to Zimmerman by an American friend of Zimmerman's. Over lunch, Mikheyev told the congressional aide that he thought the US and the Soviet Union were on a collision course, and that he wanted to obtain a certain document, apparently pertaining to US-Soviet relations, which was available only at the highest levels of the US government. Zimmerman was told by the FBI to tell the Soviet that the document was highly classified. But Mikheyev continued to pursue the matter.

''All the time I was talking with him, I kept thinking what a nice guy he seemed to be,'' says Zimmerman. ''He tried to appeal to my conscience. . . . He said he was looking for a way to stop this collision.''